> On 15 Jun., 22:24, Virgil <Vir...@home.esc> wrote:> > > > Note that it is possible to have an uncomputable number whose decimal> > expansion has infinitely many known places, so long as it has at least> > one unknown place.> > That is mathematically wrong.

It may not match every definition of 'uncomputable', but otherwise it is right.

> Nevertheless: Every number that can be determined, i.e., that is a> number, belongs to a countable set.

If every set of numbers is provably countable, that means that for every set there is a constructable surjection from N to that set, and for any such surjection, Cantor proves there is a real number not covered.